A body falls for 4s from rest. If the acceleration due to gravity of earth ceases to act, then the velocity and distance it travels in the next 3sec is

Options

A. 40 m/s , 120 m
B. 30 m/s , 400 m
C. 50 m/s, 50 m
D. 20 m/s , 60 m

Answer

To solve the problem step by step, we will break it down into parts.

### Step 1: Determine the velocity of the body after 4 seconds of free fall
The body falls for 4 seconds from rest. We can use the first equation of motion to find the final velocity (v) after this time.

The equation is:
\[ v = u + at \]

Where:
- \( u \) = initial velocity = 0 (since it starts from rest)
- \( a \) = acceleration due to gravity = \( g \) (approximately \( 10 \, \text{m/s}^2 \))
- \( t \) = time = 4 seconds

Substituting the values:
\[ v = 0 + (10 \, \text{m/s}^2)(4 \, \text{s}) \]
\[ v = 40 \, \text{m/s} \]

### Step 2: Analyze the motion after the acceleration due to gravity ceases
After the 4 seconds, the acceleration due to gravity ceases to act. Therefore, the body will continue to move with a constant velocity of \( 40 \, \text{m/s} \) for the next 3 seconds.

### Step 3: Calculate the distance traveled in the next 3 seconds
Since the body is now moving with uniform velocity, we can calculate the distance (s) traveled using the formula:
\[ s = vt \]

Where:
- \( v \) = velocity = \( 40 \, \text{m/s} \)
- \( t \) = time = 3 seconds

Substituting the values:
\[ s = (40 \, \text{m/s})(3 \, \text{s}) \]
\[ s = 120 \, \text{m} \]

### Final Results
- The velocity of the body after 4 seconds is \( 40 \, \text{m/s} \).
- The distance traveled in the next 3 seconds is \( 120 \, \text{m} \).

### Summary
- Velocity after 4 seconds: \( 40 \, \text{m/s} \)
- Distance traveled in the next 3 seconds: \( 120 \, \text{m} \)

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